Text-to-image synthesis aims to generate realistic images conditioned on text descriptions. To fuse text information into synthesized images, conditional affine transformations (CATs), such as conditional batch normalization (CBN) and conditional instance normalization (CIN), are usually used to predict batch statistics of different layers. However, ordinary CAT blocks control the batch statistics independently disregarding the consistency among neighboring layers. To address the above issue, we propose a new fusion approach names recurrent affine transformation (RAT) for synthesizing images conditioned on text information. RAT connects all the CAT blocks with recurrent connections for explicitly fitting the temporal consistency between CAT blocks. To verify the effectiveness of RAT, we propose a novel visualization method to show how generative adversarial network (GAN) fuses conditional information. Our microscopic and macroscopic visualizations not only demonstrate the effectiveness of RAT but also turn out to be a useful perspective to analyze how GAN fuses conditional information. In addition, we propose a more stable spatial attention mechanism for the discriminator, which helps the text description to supervise the generator to synthesize more relevant image contents. Extensive experiments on the CUB, Oxford-102, and COCO datasets demonstrate the proposed model's superiority in comparison to state-of-the-art models. Our code is available on https://github.com/senmaoy/RAT-GAN .

Owing to the availability of data of one biological phenomenon at different levels/scales, modelling of biological systems is moving from single level/scale to multiple levels/scales, which introduces a number of challenges. Coloured Petri nets (ColPNs) have been successfully applied to multilevel, multiscale and multidimensional modelling of some biological systems, addressing many of these challenges. In this article, we first review the basics of ColPNs and some popular extensions, and then their applications for multilevel, multiscale and multidimensional modelling of biological systems. This understanding of how to use ColPNs for modelling biological systems will assist readers in selecting appropriate ColPN classes for specific modelling circumstances.

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.